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Permeability Estimation Directly From Logging-While-Drilling Induced PolarizationData

Fiandaca, G.; Maurya, P.K.; Balbarini, Nicola; Hördt, A.; Christiansen, A.V.; Foged, N.; Bjerg, PoulLøgstrup; Auken, E.

Published in:Water Resources Research

Link to article, DOI:10.1002/2017WR022411

Publication date:2018

Document VersionPublisher's PDF, also known as Version of record

Link back to DTU Orbit

Citation (APA):Fiandaca, G., Maurya, P. K., Balbarini, N., Hördt, A., Christiansen, A. V., Foged, N., Bjerg, P. L., & Auken, E.(2018). Permeability Estimation Directly From Logging-While-Drilling Induced Polarization Data. WaterResources Research, 54(4), 2851-2870. https://doi.org/10.1002/2017WR022411

RESEARCH ARTICLE10.1002/2017WR022411

Permeability Estimation Directly From Logging-While-DrillingInduced Polarization DataG. Fiandaca1 , P. K. Maurya1 , N. Balbarini2 , A. H€ordt3 , A. V. Christiansen1 ,N. Foged1, P. L. Bjerg2 , and E. Auken1

1HydroGeophysics Group, Department of Geoscience, Aarhus University, Aarhus C, Denmark, 2Department ofEnvironmental Engineering, Technical University of Denmark, Lyngby, Denmark, 3Institute for Geophysik undextraterrestrische Physik, TU Braunschweig, Braunschweig, Germany

Abstract In this study, we present the prediction of permeability from time domain spectral inducedpolarization (IP) data, measured in boreholes on undisturbed formations using the El-log logging-while-dril-ling technique. We collected El-log data and hydraulic properties on unconsolidated Quaternary and Mio-cene deposits in boreholes at three locations at a field site in Denmark, characterized by different electricalwater conductivity and chemistry. The high vertical resolution of the El-log technique matches the lithologi-cal variability at the site, minimizing ambiguity in the interpretation originating from resolution issues. Thepermeability values were computed from IP data using a laboratory-derived empirical relationship pre-sented in a recent study for saturated unconsolidated sediments, without any further calibration. A verygood correlation, within 1 order of magnitude, was found between the IP-derived permeability estimatesand those derived using grain size analyses and slug tests, with similar depth trends and permeability con-trasts. Furthermore, the effect of water conductivity on the IP-derived permeability estimations was foundnegligible in comparison to the permeability uncertainties estimated from the inversion and the laboratory-derived empirical relationship.

1. Introduction

The permeability (k), or its counterpart hydraulic conductivity, is a key parameter in hydrogeological investi-gations as it is a main requirement for groundwater flow characterization within an aquifer. Traditionally,the spatial distribution of k is estimated by grain size analyses of samples from drillings or with in situ slugtests in screened boreholes. These methods are expensive, time consuming, and sometimes unreliable(Rosas et al., 2014). For example, grain size analysis (GSA) requires good quality of soil or sediment sampleswhich does not necessarily represent the aquifer heterogeneity and can be disrupted or washed out duringthe drilling process. Moreover, it is based on some empirical equations which have their own limitations(Rosas et al., 2014). In comparison to GSA, slug-test (ST) measurements are more reliable, but they are stilllocal measurements and are prone to wellbore skin effects (Hinsby et al., 1992).

As an alternative approach, geophysical methods have been increasingly used for permeability mapping,and spectral induced polarization (SIP) has indicated its potential in permeability estimation in the labora-tory (e.g., Binley et al., 2005; B€orner et al., 1996; Revil & Florsch, 2010; Slater, 2007; Weller et al., 2015a; Zisseret al., 2010).

SIP is a geophysical technique used to measure the diffusion-controlled polarization processes at the inter-face between mineral grains and the pore fluid. The IP response is usually represented as complex conduc-tivity, r�5 rbulk1r0surf

� �1ir00surf , where rbulk is the bulk conduction through the pore volume, r0surf represents

the surface conduction along the mineral-fluid interface, and the imaginary part r00surf is related to the polari-zation of the charges at this interface (Slater & Lesmes, 2002b). The imaginary part r00surf (hereafter referredto as r00) is commonly used to represent the magnitude of the interfacial polarization.

Models describing the relationships between polarization response and permeability can be categorized intwo classes. The first class is based on r00 and the second class is based on relaxation time, a quantity usedto represent the characteristic hydraulic length scale (Revil, 2012). The relaxation time can be extracted forinstance by Debye-Decomposition (Nordsiek & Weller, 2008) or from Cole-Cole inversion (Florsch et al.,

Key Points:� Permeability prediction from time

domain spectral induced polarizationdata measured in the undisturbedformation using El-log technique� Laboratory-derived empirical

equations for unconsolidatedsediments were used, without anyfurther calibration� IP-derived permeability within one

decade from GSA and slug-testestimates, with weak effect ofelectrical water conductivity

Supporting Information:� Supporting Information S1� Table S1� Table S2� Table S3� Table S4

Correspondence to:G. Fiandaca,gianluca.fiandaca@geo.au.dk

Citation:Fiandaca, G., Maurya, P. K., Balbarini, N.,H€ordt, A., Christiansen, A. V., Foged, N.,et al. (2018). Permeability estimationdirectly from logging-while-drillinginduced polarization data. WaterResources Research, 54, 2851–2870.https://doi.org/10.1002/2017WR022411

Received 19 DEC 2017

Accepted 21 MAR 2018

Accepted article online 26 MAR 2018

Published online 13 APR 2018

VC 2018. American Geophysical Union.

All Rights Reserved.

FIANDACA ET AL. 2851

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2014) of complex conductivity spectra. In our study the r00-based approach was used. The premise of esti-mating k using r00 is based on its strong relationship with surface area normalized to the pore volume (Spor ),which holds the fundamental basis for derived empirical relationships between k and r00 in laboratory stud-ies (B€orner et al., 1996; Slater & Lesmes, 2002a; Weller et al., 2015a).

Despite the potential shown by the IP method for estimating permeability in the laboratory, the effective-ness of the method at field scale has yet to be extensively evaluated. Three main issues are reoccurring inthe few attempts published so far: (1) the lack of spatial resolution in the geophysical imaging at the scaleof the field variability (e.g., Attwa & G€unther, 2013; Binley et al., 2016; H€ordt et al., 2009; Maurya et al., 2018);(2) the use of site-specific relations between IP properties and permeability (e.g., Attwa & G€unther, 2013;B€orner et al., 1996; H€ordt et al., 2007; Kemna et al., 2004); (3) the use of relations between IP properties andpermeability derived for lithologies different from the ones present in the field (e.g., H€ordt et al., 2009;Weller & B€orner, 1996).

The aim of this work is to evaluate the capability of the IP method in predicting permeability at field scale,in presence of heterogeneity in both lithology and water chemistry, overcoming the above mentioned limi-tations. First, the SIP data were acquired in situ through the El-log drilling technique (Sørensen & Larsen,1999) extended to time domain (TD) SIP measurements (Gazoty et al., 2012). The technique measures TDSIP data while drilling, through electrodes embedded in the stem auger. No drilling mud or borehole back-filling are used, allowing for measurements on ‘‘undisturbed’’ formations. Hence, the high vertical resolutionof the El-log technique allows for ruling out a limited spatial resolution from the possible ambiguities in theinterpretation of the IP-derived k-estimates. Secondly, permeability was estimated using the r00-basedapproach of Weller et al. (2015a) for unconsolidated materials, derived from an extensive data set of labora-tory data, without any further site-specific calibration. Permeability estimations from small-scale boreholemeasurements (down to 5 m) are presented also in Weller and B€orner (1996) and B€orner et al. (1996) but, aspreviously stated, the relation between IP properties and permeability was calibrated in B€orner et al. (1996),while in Weller and B€orner (1996) relations derived for lithologies different from the ones present in thefield were used (and the correlation between IP-derived permeability and the grain size analysis was notoptimal).

The El-log TD SIP data were collected in three locations in an unconsolidated aquifer with Quaternary andMiocene deposits in the Grindsted area in the south-western part of Denmark (Figure 1). The aquifer southof the stream is contaminated by a leachate plume from the former Grindsted landfill, while the aquifernorth of the stream is affected by contamination from a former pharmaceutical factory (Rønde et al., 2017;Sonne et al., 2017). Significant variations in electrical water conductivity and inorganic water chemistry arepresent among the three El-logs (water conductivity: here and throughout the manuscript conductivityalways refers to electrical water conductivity). Consequently, the effect of water conductivity/chemistry onthe quality of the IP-derived k-estimates is studied.

The decays were carefully processed and inverted using the inversion algorithm by Fiandaca et al. (2012),that supports the modeling of full decay and waveform. The IP-derived permeability values were comparedto an extensive set of independent permeability estimates, composed by 54 GSA estimates on sedimentsamples and 9 ST measurements. Finally, the surface area per unit volume, Spor, was measured on 25 sam-ples with the BET method (Brunauer et al., 1938) and compared to the IP-derived values.

2. Material and Methods

2.1. Study AreaThe study was carried out in an aquifer near the Grindsted landfill situated in an outwash plain west of themain stationary line of the Weichselian glaciation (Figure 1). The upper Quaternary sediments in the aquiferconsists mainly of medium to coarse meltwater sand (Heron et al., 1998), while the underlying Miocenesediments are primarily medium to fine mica-rich sand with interbedded thin clay and lignite layers (Heronet al., 1998). The water table is located 1–3 m below the terrain. The hydraulic gradient shows an overallwesterly flow direction toward the Grindsted stream (Figure 1). The Grindsted landfill has historical depositsof municipal solid waste, industrial waste, sewage treatment waste, and demolition waste (Kjeldsen et al.,1998). There is no liner or leachate collection beneath the landfill.

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El-log E1 is situated south of the landfill (Figure 1) and expected to be unaffected by the landfill leachateplume (Bjerg et al., 1995). El-log E2 is placed in the core of the landfill leachate plume in an area highly con-taminated with organic and inorganic contaminants (see supporting information Table S1). This is alsoreflected in a recent mapping of the plume by using 2-D and 3-D electrical resistivity tomography (Mauryaet al., 2017). El-log E3 is placed in similar deposits north of the Grindsted stream as shown in Figure 1(Maurya et al., 2018). Each El-log has a corresponding borehole (Bh1–Bh3) drilled for lithological descriptionand collection of water samples, and a sediment core (Sc1) was collected next to E1 as well. The permeabil-ity estimation from IP data has an underlying assumption for its applicability in contaminated sites: the con-tamination should have neither IP nor DC signature, except for the effect of water conductivity. Thisrequirement is not always fulfilled, for instance in subsurface settings contaminated with NAPLs (Chen et al.,2012; Johansson et al., 2015; e.g., Orozco et al., 2011, 2012). However, the IP signature is usually significantonly where the contaminants are present in concentrations close to the saturation point (e.g., above 1 g/Lfor BTEX in Orozco et al. (2012)). At the stream site the concentrations of organic compounds are muchbelow this concentration level (Rønde et al., 2017) and will not have any influence on IP or DC signature. Atthe landfill site, there is no presence of NAPL in the plume. The landfill is in the methanogenic phase (Kjeld-sen et al., 1998) and the organic matter/dissolved organic carbon is expected to be dominated by fully dis-solved humic like compounds without effect on IP signals (Christensen et al., 2001).

Figure 1. Location of the study area with positions of the El-logs shown with the black dots. The blue dot shows the posi-tion of the study site in the map of Denmark.

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2.2. El-Log TechniqueThe El-log is a high resolution drilling technique used in groundwater and environmental investigations forunconsolidated sediments. The El-log technique provides ‘‘while-drilling’’ measurements of the direct cur-rent (DC) resistivity, TD SIP decays and gamma radiation (Gazoty et al., 2012; Sørensen & Larsen, 1999).Apparent resistivity and chargeability are measured using the electrodes integrated in the hollow stemauger (Figure 2). The electrodes are embedded in insulating material and the gamma probe is located closeto the drilling head. Gamma probe and electrodes are connected to a control unit on the surface throughthe cables passing in the hollow stem auger. The control unit receives the signal from gamma probe andsends the data to a field PC and passes the electrode connection to the multi-channel resistivity meter. APole-Pole configuration is used for measurements with two potential and one current electrodes in theauger (spaced 0.2 m). Two electrodes are placed on the surface as remote potential and current electrodesand are connected to the control unit. Measurements can be performed while the drill stem is rotating ifgood electrode contact is maintained. Alternatively, the drill rotation is paused briefly at regular depth

Figure 2. Sketch of principal components of the El-log equipment; a 5 20 cm.

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intervals to obtain measurements. In addition to the logging equipment, a water sampler device is alsolocated inside the auger, with inlets close to the drill tip and is connected through the tubes to the surface.

2.3. Acquisition, Processing, and Inversion of El-Log TD SIP DataFor recording of TD SIP data, we used the Terrameter-LS instrument (ABEM) and full-waveform data wererecorded at a sampling rate of 3750 Hz. In borehole E2 and E3, a 4 second on-time and 4 s off-time cyclewas used whereas a 2 s on-time and off-time was used in E1. A 50% duty cycle (50% on-time and 50% off-time) waveform was used in E2 and E3, while both 50% duty cycle and 100% duty cycle (no off-time) wave-forms (Olsson et al., 2015) were measured in E1 (except 5 m data from depth 16 to 21 m, measured onlywith 100% duty cycle because of an instrumental failure that prevented the acquisition of the 50% dutycycle data). The acquisition parameters in the boreholes are slightly different from each other, because theloggings in E2 and E3 were originally not done with the purpose of estimating permeability. Only after thepotential had been recognized, the data in E2 and E3 were analyzed for permeability estimation. The con-clusions will not be affected by the differences in the acquisition settings, because the current waveform istaken into account in the forward algorithm and the permeability estimation will be based on well-resolvedinversion parameters. In any case, for minimizing the differences in the analyses of the three boreholes, the50% duty cycle data were used for E1, where possible.

A maximum current of 200 mA was used. The resistivity and IP decay data were measured while the augerwas moving and rotating.

The full-waveform data were processed for harmonic denoising and removal of background potential driftfollowing Olsson et al. (2016). These processed data were then gated using 33 logarithmically spacedtapered time windows in the interval 1–3,980 ms (gate widths starting at 0.26 ms, ending at 820 ms) for the4 s pulses and in the interval 1–1,980 ms (gate width 0.26–420 ms) for the 2 s pulses. The data were thenimported to the Aarhus Workbench software (www.aarhusgeosoftware.dk) for further manual editing andprocessing. In the manual processing, each individual IP decay curve was inspected and noisy data points,for example due to electrode contact problems, were removed. Generally, the first usable gate was foundto be around 2–3 ms and the average number of gates was found to be around 30, equivalent of about 3decades of spectral content.

The inversion of El-log TD SIP data was performed using the AarhusInv (Auken et al., 2014) code, an inte-grated modeling and inversion code for electrical and electromagnetic data. Forward modeling of El-log TDSIP data follows the recursive formulation by Sato (2000) and takes into account the transmitter waveformand the receiver transfer function (Fiandaca et al., 2012).

In the model space, the frequency-dependent complex conductivity r� is described through a reparameteri-zation of the Cole-Cole model, namely the bulk and (maximum) imaginary conductivity (BIC) Cole-Colemodel, developed explicitly for being used in permeability estimation and described in details in the nextsection. Considering the 0.2 m spacing between the current and potential electrodes in the auger, a 0.2 mvertical discretization was used in the E-log inversion models.

2.4. Parameterization of Induced PolarizationThe Cole-Cole model in its conductivity form is expressed as (e.g., Tarasov & Titov, 2013)

r� fð Þ5r0 11m0

12m012

1

11 i2pfsrð ÞC

!" #(1)

where r� is the complex conductivity, r0 is the DC conductivity, m0 is the intrinsic chargeability, sr isthe relaxation time, C is the frequency exponent, f is the frequency, and i is the imaginary unit. In equa-tion (1), the m0 and C parameters are strongly correlated, and thus poorly resolved in the inversion(Fiandaca et al., 2017, 2018). In order to reduce the parameter correlation, and hence improve the inver-sion results, Fiandaca et al. (2018) introduced the maximum imaginary conductivity (MIC) model, inwhich m0 is replaced by maximum imaginary conductivity r00max of the Cole-Cole spectrum (Figure 3)and the model space mMIC becomes

mMIC5 r0; r00max; sr; C

� �(2)

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In equation (2), r0 is the DC conductivity, which is the sum of the bulk conductivity rbulk and the DC surfaceconductivity r0surf f 50ð Þ (Weller & B€orner, 1996):

r05rbulk1r0surf f 50ð Þ5 rW

F1r0surf f 50ð Þ (3)

where in the last term of the equality rbulk is expressed through the formation factor F and the water con-ductivity rW , following Archie’s law (Archie, 1942). When imaging the DC conductivity (or, equivalently, DCresistivity), as in the MIC model, the bulk and surface conduction are not discriminated.

To overcome this limitation the BIC model has been developed, in which we make use of the petrophysicalrelation between the real and imaginary components of the surface conductivity described in Weller et al.(2013):

r005l � r0surf (4)

with l50:042 6 0:022 (dimensionless). The relation in equation (4) was obtained from a database of 63 sam-ples of sandstone and unconsolidated sediments, covering nine independent investigations, using multisa-linity resistivity measurements and r00 measurements at a frequency f ffi 1 Hz. The variability of theproportionality with frequency is not discussed in Weller et al. (2013); considering that the (surface) imagi-nary conductivity of the Cole-Cole model reaches a maximum r00max at the frequency f 51=2psr , we decidedto enforce in the BIC model the proportionality between the real and imaginary surface conductivity at thisfrequency (which is not necessarily 1 Hz):

r00 f 51=2psrð Þ5r00max5l � r0surf f 51=2psrð Þ (5)

This is a conservative choice: in this way, the ratio between the surface imaginary conductivity and real con-ductivity never exceeds the factor of equation (4). On the contrary, enforcing the proportionality at f 51 Hzwould imply a ratio well above l at the peak frequency f 51=2psr for models with sr � 1.

Enforcing the relation of equation (5) in the MIC Cole-Cole model, it is possible to define the BIC model withmodel space mBIC defined in terms of the bulk conductivity rbulk , the maximum imaginary conductivity r00max

and the other two classic Cole-Cole parameters sr and C:

mBIC5 rbulk ; r00max; sr; C

� �(6)

Therefore, contrary to the MIC model, with the BIC parameterization, the bulk conductivity is separatedfrom the DC surface conductivity. This allows for the estimation of the formation factor F directly from theinversion parameters, when the water conductivity is known.

Figure 3. Spectrum of the BIC model computed using rbulk510 mS=m; r00max50:1 mS=m; sr50:1 s and C 5 0:5. (a) Realconductivity r0(black curve), obtained as the sum of the bulk conductivity rbulk (magenta curve) and the surface real con-ductivity r0surf . The water-conductivity value rw with formation factor F 5 5 is also shown. (b) Imaginary conductivity r00 .Modified from Maurya et al. (2018).

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For any given set of parameters of the BIC model, it is possible to derive the corresponding Cole-Coleparameters through simple algebraic relations, and to compute the complex conductivity at any frequencythrough equation (1). Figure 3 shows the spectrum of the BIC model defined by the parameter valuesrbulk510mS=m;r00max5 0:1mS=m; sr50:1 s; C50:5� �

. The r0 and m0 values of the corresponding Cole-Cole model are r0512:1 mS=m and m0538:2 mV=V, respectively.

2.5. Estimation of Permeability and Spor

2.5.1. Permeability From Grain Size Analysis and Slug TestsTraditional 63 mm wells (Bh1–Bh3) were installed next to each El-log (E1–E3) using cable tool bailer drilling.Samples were collected every 0.5 m for geological characterization and grain size analyses. Each well hasmultiple 1 m long screens for collecting water samples and performing slug tests. Note that the vertical dis-cretization of the traditional wells is coarser than the 0.2 m vertical discretization of the El-log retrievedmodels. In addition, sediment cores (Sc1) were collected in PVC liners by the GeoProbe sampling systemclose to El-log E1. The cores were split in half for detailed geological characterization and subsampled forlaboratory analysis.

Grain size analysis (GSA) was performed on selected soil samples from the cores (Sc1 next to E1) and sam-pling from drilling of the traditional boreholes (Bh2 and Bh3) using sieving, for particle size between 2and 0.063 mm, and laser diffractometer (Mastersizer Hydro 2000SM), for particle size between 63 and0.02 mm (Switzer & Pile, 2015). The grain size distribution curve was used to estimate the permeability.Many approaches have been suggested for this purpose and the calculated permeability can changeorders of magnitudes between the various approaches (Devlin, 2015). Thus, several methods wereapplied on each sample, depending on the properties of the sample, and the permeability values andtheir uncertainty were computed through the geometric mean and the standard deviation of the differ-ent estimations of the applicable methods. The methods used for the GSA permeability estimations wereselected from the review by Devlin (2015) and are Hazen simplified (Hazen, 1892), Slichter (Slichter, 1899),Terzaghi (Terzaghi, 1925), Beyer (Beyer, 1964), Sauerbrei (Vukovic & Soro, 1992), Kr€uger (Kr€uger, 1918),Kozeny-Carman (Kozeny, 1953), Zunker (Zunker, 1930), United States Bureau of Reclamation (Białas,1966), Barr (Barr, 2001), Alyamani and Sen (Alyamani & Sen, 1993), Chapuis (Chapuis, 2004), and Krumbeinand Monk (Krumbein & Monk, 1943). Not all samples qualify for all methods, and thus the number ofmethods to calculate the average varies between 2 and 13. On average, the standard deviation of allmethods on all sample is 0.3 decades (supporting information Table S2), indicating that the choice of thequalified methods is not crucial and the proposed approach should give robust estimates of permeabilityvalues and standard deviations. Supporting information Table S3 presents the permeability estimates forall the GSA methods adopted in this study.

Slug tests were performed with a vacuum method developed for measuring local permeability in an uncon-fined sandy aquifer (Hinsby et al., 1992). The method consists of raising the water table by using a vacuumpump and monitoring the decrease in water table over time with a 1 s time interval. The groundwater tablefalling curve was analyzed in AQTESOLV using Bouwer and Rice’s method for partially penetrating wells inunconfined aquifers (Bouwer & Rice, 1976), Hvorslev (1951) for partially penetrating wells in confined aqui-fer, and Springer and Gelhar (1991) when oscillatory responses were observed in the slug test. Two slugtests were performed at each screen and the value of permeability used for comparison was calculated byaveraging the result of the two tests. In all cases, they agreed well. Values of slug tests are provided in sup-porting information Table S4.2.5.2. Surface Area per Unit Volume (Spor) Estimates With BETThe specific surface area was measured on the selected samples from the sediment core (Sc1) using theBrunauer, Emmett, and Teller (BET) gas adsorption method (Brunauer et al., 1938; Santamarina et al., 2002).The surface area was measured on a dry sample using N2 gas (Micromeritics FlowPrep 060). Since themethod required a dry sample, the surface area of interlayer surfaces in swelling clays is only partiallymeasured by the method (Santamarina et al., 2002). Values of Spor are provided in supporting informationTable S5.2.5.3. Permeability and Spor From Spectral IPMost of the early works for estimating the permeability (k) were based on a Kozeny-Carman type equationgiven as

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k5/

aS2por T

(7)

where / is the porosity, T is a pore capillary tortuosity factor, and a is a shape factor. Considering the sensi-tivity of induced polarization to Spor , a number of efforts have been made to reformulate the equation (7)for more direct use with SIP modeling (Slater, 2007). For example the ratio T=/ can be replaced by forma-tion factor F (5Tel=/), assuming that electrical tortuosity (Tel) is equal to hydraulic tortuosity (T). Such a typeof model was proposed by B€orner et al. (1996):

k5b

FScpor

(8)

where b and c are empirical constants and F is the formation factor. The two unknowns, F and Spor ; can beestimated using the SIP measurements. Recently, Weller et al. (2015a) investigated a data base consisting of114 globally collected samples. They avoided the indirect k-estimation through Spor and suggested directcorrelations between k and the imaginary conductivity r00, measured with a NaCl solution with standard-ized electrical conductivity rf 5100 mS=m at a frequency f ffi 1 Hz. For unconsolidated (saturated) sedi-ments, they proposed two empirical equations:

k51:08 3 10213

F1:12� r00 rfð Þð Þ2:27 (9)

k53:47 3 102163r0 rfð Þð Þ1:11

r00 rfð Þð Þ2:41 (10)

where k is given in m2, r0 and r00 are given in mS/m, and F is dimensionless. Equation (9), likewise equation(8), depends on the formation factor F, while equation (10) depends on the DC conductivity r0. The assump-tion in equation (10) is that the apparent formation factor F05 rf

r0 rfð Þ can be used in permeability estimationinstead of the true formation factor F, which is rarely available for most practical field applications in hydro-geophysics. This assumption was found valid by Weller et al. (2015a) for unconsolidated samples, while forconsolidated samples the prediction based on F was superior (because the exponents of F and r0 in the for-mula equivalent to equations (9) and (10) are higher for consolidated samples, and the formation factorplays a bigger role in the permeability estimation).

Although the explicit calculation of Spor is no longer necessary to estimate k from equations (9) and (10),Spor is still a macroscopic parameter that can be measured in the laboratory and the relation between r00

and Spor is the theoretical basis of the permeability estimation. Therefore, we also estimate Spor using the fol-lowing relationship with r00:

r005CpSpor (11)

where Cp is called the specific polarizability (Weller et al., 2010).2.5.4. Permeability Estimation From Inversion Parameters and Effect of Water ConductivityThe empirical equations (9) and (10) link the permeability, which is a function of the material structure only,to the electrical properties of the material, which depend also on the electrical water conductivity and, forthe surface properties, also on the water chemistry. This is why the equations are derived from a standard-ized water solution (i.e., NaCl solution with electrical conductivity rf 5100mS=m). In field surveys, the watersolution can be assumed to be known, but its conductivity will generally not equal 100mS=m nor the solutewill be only NaCl.

The dependency of the imaginary surface conductivity on the water solution for consolidated and uncon-solidated sediments can be expressed as (Weller & Slater, 2012; Weller et al., 2011, 2015a)

r00 rwð Þ5r00 rfð Þ31

Cf3

rw

rf

� �a

(12)

where rf 5100 mS=m represents the electrical conductivity of a reference NaCl solution, Cf accounts for thepossible differences in ionic species between the reference and actual solution and the exponent adepends on the material. Weller et al. (2011) found a50:5 for sandstones, and Weller et al. (2015a) used a5

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0:5 for both sandstones and unconsolidated samples in the correction for water conductivity in permeabil-ity estimations. Nevertheless, Weller and Slater (2012) showed a certain variability in the exponent a for thecorrection on unconsolidated samples, with average value and standard deviation equal to a50:37 6 0:12(these estimates are not shown explicitly in Weller and Slater (2012), but can be retrieved from the full setof values shown in Table 1 therein).

In order to use equation (9) from the inversions of field data, as we do in this study, the formation factorand the imaginary surface conductivity r00 (for standardized solution at frequency f 51Hz) need to be esti-mated. Remember that through the BIC model as defined through equations (3–6), we obtain the bulk elec-trical conductivity, which does not include surface conductivity any more. We can thus calculate theformation factor directly from F5 rW

rbulk.

Using equation (12) with a50:37 and calculating the formation factor as explained above, we obtain

F1:12 3 r00 rfð Þð Þ2:275

5rw

rbulk

� �1:12

3 r00 rwð Þ3 Cf 3rf

rw

� �0:37 !2:27

5Cf2:27 3 rf

0:84 3r00 rwð Þð Þ2:27

rbulk rwð Þð Þ1:12 3 rw0:285

54:78 3 101 3 Cf2:27 3

r00 rwð Þð Þ2:27

rbulk rwð Þð Þ1:12 3 rw0:28 (13)

where in the last equality rf 5100 mS=m was used. The water-conductivity correction rw0:28 compensates the

dependency of r00 rwð Þð Þ2:27

rbulk rwð Þð Þ1:12 on the water conductivity rw . Equation (13), and henceforth equation (9), can be eval-

uated from the inversion parameters of the BIC model and from the knowledge of the water solution.

Note that the dependence of the k-estimation on groundwater conductivity is weak. Indeed, the power of0.28 for rw in equation (13) means that, for example, a 10-fold variation in water conductivity causes lessthan a 2-fold variation in IP-estimated permeability. The effect of the uncertainty of the exponent a of equa-tion (12) on equation (13), as well as the importance of the water-conductivity correction in comparison tothe other uncertainties in the IP-derived permeability estimation, is discussed in detail in the next paragraphand in section 3.

For the correction of the water chemistry, Weller et al. (2011) suggest Cf 52 for CaCl2 and Cf 51 for NaCl; forother ions, no suggestion was made. Realizing that the original suggestion is based on a sparse data setand that numerous cations and anions are present in the field-collected water samples with varying molec-ular concentration, it is difficult to apply an appropriate correction. Therefore, in our k-estimation the correc-tion factor Cf was not accounted for.

For the evaluation of equation (13), the imaginary conductivity at frequency f 51 Hz can be computed fromthe inversion parameters r00max; sr; C

� �. Actually, as it is shown in section 3, minor differences exist between

r00max and r00 f 51 Hzð Þ, so r00max is used in equation (13) in our computations, also because this simplifies thepropagation of the inversion parameter uncertainty into the parameter uncertainty.

As an alternative to equations (9) and (13) and the inversion in terms of the BIC parameters of equation (6),it is possible to derive the permeability from equations (10) and (12) and the inversion in terms of the MICparameters of equation (2), i.e., it is possible to use r0 instead of rbulk . In this study, we prefer to follow thefirst approach for two reasons: (i) the effect of surface conductivity in the estimation of the formation factoris taken into account (i.e., an estimate of the true formation factor F is used instead of an estimate of theapparent formation factor F0); (ii) the use of the BIC model instead of the MIC model is better suited for per-meability estimation from surface IP data, as shown recently by Maurya et al. (2018). In fact, the use of theBIC model in 2-D/3-D imaging practically imposes a geometrical constraint between the spatial distributionof the inverted imaginary conductivity r00 and the spatial distribution of the total DC conductivity r0 sec-tion, so that a chargeable area in the inversion model is also conductive. On the contrary, when r0surf gives anegligible contribution to r0, no geometrical constraint is enforced between the r00 and r0 spatial distribu-tions and the BIC and MIC models give equivalent results. This feature reduces the equivalences in the r0

imaging and helps in retrieving inversion models more representative of the site geology, and henceforthbetter permeability estimations (Maurya et al., 2018). However, in this study, the high vertical resolution of

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the El-log technique avoids equivalence problems in the r0 estimation, and the permeability estimatesretrieved by the MIC and BIC inversions are of comparable quality (results not shown for brevity).2.5.5. Evaluation of Prediction Quality and Uncertainty on Permeability EstimatesThe total uncertainty on the IP-derived permeability estimation depends on the uncertainties of the pet-rophysical relations, as well as on the uncertainty of the inversion parameters used in the computations.The prediction quality of equations (9) and (10) was defined by Weller et al (2015a) in terms of the aver-age absolute deviation (in log space) between the IP-derived permeability kIP and measured permeabil-ity kmeas:

d51N

3XN

i51jlog10 kIP ið Þ2log10 kmeasið Þj (14)

Using equation (9), Weller et al (2015a) found for unconsolidated samples a value d50:386, which impliesthat the IP-derived permeability estimates are on average accurate within an uncertainty factor (UF) of

UFIP510d5100:386 ffi 2:4 (15)

In order to estimate the uncertainty of the correction of the imaginary conductivity due to the variablewater conductivity, the standard deviation STDa of the exponent a of equation (12) is used. Indeed, the con-fidence interval of the permeability estimates can be computed using equations (9) and (13) with the confi-dence limits of the exponent a2STDa; a1STDa½ �. This leads to an uncertainty factor of

UFrW 5rW

rf

� �0:27

(16)

Combining equations (9) and (13), the upper limit a1STDa50:49 (practically the value used and suggestedby Weller et al (2015a)) gives a total water-conductivity correction rw

0:008, while the lower limit a2STDa5

0:25 gives rw0:55. This means that in the upper limit the water-conductivity correction is practically equiva-

lent to no correction, because of the small exponent of rw , while with the lower limit the correctiondepends approximately on the square root of rW .

The final contribution to the permeability uncertainty derives from the uncertainty on the inversion parame-ters. This uncertainty can be computed from the covariance of the estimator error for linear mapping Cest

described by Tarantola and Valette (1982):

Cest5 GT C�21d G

� 21(17)

where G represents the Jacobian of the last iteration of the inversion and the diagonal matrix C�d is a modi-fied data covariance matrix. The modification consists of taking as diagonal elements C�d i; i the maximumbetween the data variances Cd i;i and the squared misfit fi2dið Þ2, where i represents the index of the datavector, di is the ith datum, and fi is the corresponding forward response. The use of C�d instead of the classicCd in equation (17) avoids to underestimate the parameter uncertainty if some data are not fitted withinthe standard deviation in the inversion process. Once the uncertainty on the inversion parameters is com-puted, the inversion-derived uncertainty on the permeability estimates can be computed as

STDkIP 5

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi@k

@rbulk3 STDrbulk

� �2

1@k@ r00

3 STDr00max

� �2s

(18)

where @k@rbulk

and @k@ r00 are the partial derivatives of the permeability formula obtained combining equations

(9) and (13), STDrbulk is the inversion uncertainty on the bulk conductivity, and STDr00maxis the inversion uncer-

tainty on the maximum imaginary conductivity. The uncertainty factor derived from the inversion uncer-tainty can then be computed as

UFinversion511STDkIP

kIP(19)

Finally, the total uncertainty on the permeability estimates is obtained multiplying the three uncertainty fac-tors of equations (15), (16), and (19):

UFtotal5UFIP 3 UFrW 3 UFinversion (20)

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3. Results

3.1. Inversion Models and Data FitFigure 4 presents the inversion models of the three El-logs, for all inversion parameters, together with theparameter uncertainty computed through equation (17), while Figure 5 shows the fit of the DC data and ofrepresentative IP decays of the three inversions. The data standard deviations used in the inversion and forthe computation of the parameter uncertainty were 1% on resistivity and 10% on each gate of the IP

Figure 4. Inversion models for (top) El-log E1, (middle) E2, and (bottom) E3. All four inversion parameters are shown in the four figure columns (thick black lines),together with the confidence interval defined through equation (17) (thin black lines). In the second column, the imaginary conductivity r00 f 51 Hzð Þ, computedfrom the parameters r00max; sr; C

� �, is shown in red (but r00 f 51 Hzð Þ is visible only where it differs significantly from r00max).

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decays, plus a voltage noise floor Vnoise50:1 mV (see Olsson et al. (2015) for details on the computation ofthe total data uncertainty from Vnoise and the relative standard deviation). In Figure 4, it is seen that r00max is awell-resolved inversion parameter, with uncertainty comparable to the rbulk uncertainty, while the fre-quency exponent C and, even more, the time constant sr present significantly wider confidence intervals.The small r00max uncertainty derives from the reparameterization of the Cole-Cole model: when inverting thesame data with the classic Cole-Cole model, the uncertainty on m0 is much higher, due to the high correla-tion between m0 and the frequency exponent C (Fiandaca et al., 2018; Madsen et al., 2017).

In Figure 4, the imaginary conductivity r00 at frequency f 51 Hz, computed from the inversion parametersr00max; sr; C� �

, is shown together with the r00max inversion estimates, because r00 f 51 Hzð Þ is needed inequations (9) and (13). The frequency exponent C of the Cole-Cole parameterization (equation (1)) is gener-ally small, resulting in broad spectra, so that r00 f 51 Hzð Þ and r00max are close to each other. In particular, forthis data set the (geometric) mean difference between r00 f 51 Hzð Þ and r00max ranges only from 4% (El-logE1) to 10% (El-log E3). Consequently, the difference in k-prediction using r00 f 51 Hzð Þ and r00max is on aver-age only 6% (actually, in favor of the r00max estimates), which is negligible compared to the overall scatterbetween permeability values derived from IP and GSA/ST estimates seen in the next sections. Therefore,r00max will be used instead of r00 f 51 Hzð Þ in the further calculations.

3.2. Lithology Versus rbulk ; r00max ; and Gamma RadiationThe maximum imaginary conductivity (r00max) and bulk conductivity (rbulk ), retrieved from the Cole-Cole BICinversion of TD SIP data from El-log E1 is shown in Figures 6b and 6c. The corresponding gamma logtogether with a detailed lithological log obtained from the sediment cores of Sc1 are shown in Figure 6a.The El-log TD SIP data were recorded to 27 m depth, whereas the gamma log is available to 29.5 m. Theuncertainty on the estimates of rbulk and r00max, from a linearized sensitivity analysis (Auken et al., 2014) isindicated by thin lines. A very good correlation between different sediment types and r00max can be seen.The Quaternary glacial sands (medium to coarse) exhibit on average low r00max values (�0.01 mS/m). Theboundary between the Quaternary and Tertiary sand deposits (where mica sand unit starts) are observed in9.8 m depth where a sharp transition in gamma log and r00max can be seen. The mica-rich sands (fine to

medium) shows relatively higher r00max values. Interbedded thin clayeyand silty layers (around 13 m depth) in the Tertiary formation are char-acterized by the higher gamma peaks and correlates very well with ahigh r00max: The quartz sands shows only small variations in rbulk andr00max, which is also well supported by relatively low gamma count(�10 CPS). Overall, it can be seen that the lithological variations corre-late well with r00max, which is a key parameter used for predicting k.

3.3. Correlation Between Spor and r00max

In the laboratory, a robust relationship between r00 and Spor thatexplains multiple data sets was found (Weller et al., 2010). Also,although no longer explicitly in the equations, the permeability pre-diction from r00 is implicitly based on its correlation with Spor . There-fore, we investigate this relationship in El-log E1. Figure 6d shows thecorrelation between Spor and r00max, corrected for water conductivityfollowing equation (10). As observed from the cross plot, a single Cp

value cannot explain the specific polarizability of all sediment types.This discrepancy has also been observed in the laboratory-derivedresults presented by Weller et al. (2015b) who found that if Spor ismeasured with the BET method, different values of Cp are required toexplain the relationship between Spor and r00. The relationshipsderived from their laboratory measurements for different Cp valuesare shown for reference in Figure 6d. Weller et al. (2015b) found thatsand mixed with muscovite and illite, has a higher Cp value (24 3

10212 S) than the common value of Cp (10 3 10212 s) suggested byWeller et al. (2010). We observed the same trend for mica-rich sandsin our data. For quartz-clean sands, Weller et al. (2015b) observed a

Figure 5. Data for the three El-logs (red markers: E1; magenta markers: E2; bluemarkers: E3) and corresponding data fits (black lines). (a) Apparent resistivitydata and fit. (b) IP decays and fit with current electrode C1 (see Figure 2) atdepth 5 5 m. (c) IP decays and fit with current electrode C1 at depth 5 25 m.

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lower Cp value (5.8 3 10212 S), which in our case is replicated by the glacial sands showing lower Cp values,although they are not as uniform as the laboratory sands. Overall, the estimated r00max deviates from CpSpor

less than 1 order of magnitude for most of the samples, suggesting that estimates of permeability within 1order of magnitude can be expected from IP data in this study.

3.4. Permeability Estimation From El-Log TD SIP Measurements3.4.1. Effect of Water ConductivityFigure 7 shows the variability of the water conductivity rW measured in the three El-logs and its effect onthe permeability estimates. In particular, the rW values measured on the screens close to the El-logs areshown together with: rW interpolated into depth-logs; the inverted rbulk ; the permeability, computedthrough equations (9) and (13); the confidence interval of the rW correction, computed through equation(16); the water tables levels. The permeability estimates are shown only below the water table levels,because water saturation is required in equation (9). The rW interpolation was performed individuating

Figure 6. (a) Gamma log measured in El-log-E1 and corresponding lithological log from Sc1, (b) maximum imaginary conductivity, r0 0max . (c) Bulk conductivityrbulk .The thin lines, left and right side of both parameters represent the lower and upper error bounds estimated from equation (17). (d) Correlation betweenimaginary conductivity (r0 0max ), corrected for water conductivity, and Spor measured in E1. The thin dashed black line shows the deviation of 1 order of magnitudefrom the Cp510 3 10212 S line.

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depth ranges of uniform conductivity based the rbulk trends, and assigning the rW value of the nearestmeasurement. The confidence interval of the rW correction, which practically comprises the permeabilityestimates without correction at all, is small when compared to the prediction quality of equation (9), i.e.,UFIP52.4 (equation (15)). In particular, the rW correction is practically negligible in El-log E2, i.e., the El-logplaced in the core of the landfill leachate plume, because there the water conductivity is relatively high,similar to the reference solution used in the laboratory measurements (i.e., rf 5100 mS=m). In Figure 7, thewater table levels are also shown:3.4.2. Comparison With ST and GSA EstimatesPermeability for all El-logs, computed using equations (9) and (13) with interpolated rW depth-logs, isshown in Figure 8, together with the confidence limits derived from the total uncertainty factor UFtotal ofequation (20). Furthermore, Figure 8d shows a zoom-in of El-log E2, where all the correction factors contrib-uting to UFtotal are also shown. In particular, it is seen that the smallest contribution to UFtotal is due to UFrW

(equation (16)), followed by UFinversion (equation (19)) and UFIP (equation (15)).

In all El-logs, permeability calculated using grain size analyses (GSAs) and measured with slug tests (STs) areshown for comparison. In E1, the IP-derived permeability agrees well with the GSA and ST estimates, bothquantitatively and in terms of depth trend. Overall, the estimates are within 1 order of magnitude, except inthe clay-rich sands at depths around 13.8 m (not shown in the figure), where smaller values are obtainedfrom the grain size analysis (and where the applicability of the GSA formulae is questionable, due to thehigh clay content). Also around 6–10 m depth, the IP-derived k estimates show larger deviation from GSAestimates. However, in this interval the ST estimate shows closer correspondence to IP-derived k values.Similar results can also be seen in the two other El-logs (E2 and E3). Furthermore, the ST permeability esti-mates fall always within the total uncertainty UFtotal of the IP-derived estimates, and the GSA and IP-derived

Figure 7. Effect of water conductivity rW on permeability estimation for (a) El-log E1, (b) El-log E2, and (c) El-log E3. Green triangles: rW measured in screens. Con-tinuous red lines: interpolated rW depth-logs. Dashed red lines: rbulk retrieved from the BIC inversions. Black lines: permeability kIP . Green lines: kIP limits due tothe correction for water conductivity (equation (16)). Dashed blue lines: water table levels.

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estimates almost always differ less than their combined uncertainties. Cross plots between k derived fromGSA and ST and IP-derived k are shown in Figure 9. Published data from Weller et al. (2015a), which encom-pass a wide range of unconsolidated sediments is also shown on the plot. Overall, it is seen that the perme-ability estimations from El-log TD SIP data show an agreement with the slug tests of quality comparable tothat reported by Weller et al. (2015a) on laboratory data. The average deviations (equation (14)) from theGSA k-estimates of El-log E1, E2, and E3 are dE1;GSA50:85, dE2;GSA50:63, and dE3;GSA50:70, respectively; theaverage deviation from the slug tests on all the El-logs is dST 50:23. The average deviation from both GSAand slug tests all the El-logs is dtotal50:679, practically identical to the average deviation drW 5rf 50:684obtained when using the constant value rW 5rf 5100 mS=m in equation (13), confirming the negligibleeffect of rW on the quality of the permeability estimation. For comparison, the average deviation found inWeller et al. (2015a) from laboratory measurements is dlab50:39.

4. Discussion

IP-derived k values were compared with values obtained from GSA and slug tests. A better agreement wasobtained between IP-derived k values and slug tests, than between IP and GSA estimates. When the grainsize data are used, some data points fall outside of the bounds reported by Weller et al. (2015a). This likelyreflects the limitations of the grain size estimates of permeability as much as the limitations of the IP meth-odology for k-estimation. It is worth to note that values estimated from grain size analyses are based on aspan of empirical equations, which give different permeability estimates. The variation of the GSA

Figure 8. Vertical Permeability kIP logs, estimated using equations (9) and (13), in (a) El-log E1, (b) El-log E2, and (c) El-log E3. (d) Zoom-in of El-log E2. Thick contin-uous black lines: kIP estimation. Green lines: kIP limits due to the correction for water conductivity (equation (16)). Thin black lines: kIP limits due to the inversionuncertainty (equation (19)). Magenta lines: kIP limits due to the uncertainty on the petrophysical empirical formula (equation (15)). Dashed black lines: kIP limitsdue to the total uncertainty (equation (20)). Dashed blue lines: water table levels. The horizontal error bars show the estimated uncertainty in grain size estimatedk. The vertical error bar in slug-test estimates shows top and bottom of the screen used for measurements. In Sc1, the permeability of a GSA sample around13.8 m is 4:70 310217 and is not shown in the plot.

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permeability estimates reflects the fact that the grain size distribution represents only one factor in perme-ability prediction: material with identical grain size distribution can be compacted in different ways resultingin different levels of packing, with varying porosity, and consequently varying permeability. On the contrary,IP spectra also depend on the packing procedure (Bairlein et al., 2014) and, in this sense, might be moreaccurate than the GSA analysis. Furthermore, the grain size analyses were performed on samples which notin all cases represent the actual geological layer due to losses during sampling (at least for the samples notretrieved from cores, i.e., Bh2 and Bh3). This would inevitably affect any k-prediction which relies on empiri-cal relationship with in situ structures of the sediment. All this suggests that more trust should be put onthe k values obtained through slug tests when evaluating the predictive quality of k from IP data, whichwere recorded in the undisturbed formation. In hindsight, it would have been better to design the surveywith more slug tests than grain size analyses. Therefore, it is suggested that future studies expand the com-parison to a larger data set of small-scale slug tests and other methods for in situ permeability estimation(e.g., McCall et al., 2014).

El-log E2 is located very close to the leachate plume from the Grindsted landfill and has a significantlyhigher water electrical conductivity (50–192 mS/m) compared to E1 (17–52 mS/m). Importantly, we found

Figure 9. Cross plots between measured k (kmeas) (from grain size analyses and slug tests, Bh1–3, and Sc1) and IP-derivedk (kIP) for El-logs E1, E2, and E3 using equations (9) and (13). Dashed lines show deviation of 1 order of magnitude.

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no evidence that the presence of the plume and the increased electrical conductivity affected the quality ofk-prediction from IP data, and the water-conductivity correction in the k-prediction itself is almost negligi-ble, when compared to the other uncertainties in the estimation. This is important as a wide range of waterelectrical conductivities are found in unconsolidated sediments where this method would be useful, andespecially in contaminated site investigations.

In equation (13), Cf accounts for the possible differences in ionic species in the reference and actual solu-tion, but the lack of laboratory evidence on how to correct for solution with a variety of cations and anionsprevented to apply the correction. The indication of Weller et al. (2011) about Cf (i.e., Cf 52 for CaCl2 and Cf

51 for NaCl), together with the exponent for Cf in equation (13) (i.e., 2.27), suggest a significant role of thechemical composition of the solution on the permeability prediction. Significant variations in inorganicwater chemistry are present among the three boreholes, but also vertically in each borehole. Nevertheless,the quality of k-prediction from IP data in the three El-logs is similar, without any significant bias, implyingthat Cf for solutions with a variety of cations and anions might be close to 1. The data on the chemical com-position of the water exist and are provided as supplementary document in supporting information TableS1: it will be possible to further analyze the data if new laboratory/theoretical evidence on Cf will bepresented.

Another topic that deserves more investigation is the role of the IP spectral content on the permeabilityprediction. In this study, a spectral inversion in terms of the BIC Cole-Cole model was performed, and themaximum imaginary conductivity r00max instead of r00 at 1 Hz was used in the permeability estimation,mainly because r00max and r00 at 1 Hz were very similar. However, the BIC Cole-Cole inversion allows forstudying if better correlations exist between other parameters retrieved from the IP spectrum (for instancethe normalized chargeability mn also used in Weller et al. (2015a)) and the GSA/ST estimates. This topic willbe investigated in future studies.

Remarks should be made about the applicability of the proposed method with regard to site lithology andwater saturation. Equations (9) and (13) are valid only for saturated unconsolidated sediments. Studies havebeen presented where a correction for water saturation was performed on the DC and imaginary conductiv-ity for permeability estimation (e.g., Kemna et al., 2004), but the correction for water saturation and its gen-eral applicability is beyond the scope of this study. Regarding the site lithology, in Weller et al. (2015a)equations were proposed also for sandstones, but it was found that the formation factor, instead of theimaginary conductivity, exerts the dominant control on the permeability. This presents substantial chal-lenges for the field-scale prediction of permeability from electric measurements, because an accurate esti-mation of the formation factor is required. The BIC modeling proposed in this study might help in thisrespect, because it separates the bulk conductivity from the DC surface conductivity, but its effectivenesshas yet to be evaluated on surveys carried out on sandstones.

Finally, a brief comment on the choice of the r00 approach for permeability estimation instead of theapproach based on the relaxation time (e.g., Revil et al., 2015). This choice is a natural consequence of theuncertainties of the inversion parameters presented in Figure 4: r00max is much better resolved than sr. Thisargument is even more important when considering that sr is much more difficult to be imaged from sur-face measurements instead of borehole measurements. Consequently, we believe that the r00 approach isbetter suited for field applications.

5. Conclusions

In the present study, we have shown that TD SIP can be reliably used for estimating permeability of uncon-solidated formations at field scale. For this purpose, high quality spectral TD SIP data were acquired in threeboreholes using the El-log drilling technique. A full decay time domain inversion algorithm employing areparameterized Cole-Cole model was used. Permeability was calculated by using the empirical relations forunconsolidated sediments found in the laboratory without any further calibration and the IP-derived k val-ues were compared to those estimated by grain size analyses and measured by slug tests. The k-estimationfrom IP data correlates very closely with the slug-test measurements and appears to be within 1 order ofmagnitude of k-estimates form grain size analyses data. This is a similar prediction quality as observed fromlaboratory measurements.

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Furthermore, the effect of pore water conductivity is weak in the laboratory-derived formula for the k-esti-mates, and negligible when compared to the other uncertainties in the computations, because the com-bined influence on the bulk and imaginary conductivities almost cancels out the effect in the permeabilityestimation. This theoretical prediction was confirmed in our field results, in which equivalent quality of thepermeability estimations was found in boreholes with significant differences in water conductivity, with andwithout taking into account the actual values of the water conductivity in the computations. These newfindings pave the way for detailed and inexpensive mapping of permeability on saturated, unconsolidatedsediments in the field, using both borehole and surface measurements techniques, including sites withhigh and varying pore water conductivity.

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